arXiv:2008.10965 Abstract | arXiv Analytics

arXiv:2008.10965 [math.GR]Abstract References Reviews Resources

Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups

Published 2020-08-25Version 1

We show that not every Salem number appears as the growth rate of a cocompact hyperbolic Coxeter group. We also give a new proof of the fact that the growth rates of planar hyperbolic Coxeter groups are spectral radii of Coxeter transformations, and show that this need not be the case for growth rates of hyperbolic tetrahedral Coxeter groups.

Comments: 23 pages, 3 figures

Categories: math.GR, math.GT, math.NT

Subjects: 20F55, 11R06, 22E40, 11K16

Keywords: growth rate, spectral radii, hyperbolic tetrahedral coxeter groups, cocompact hyperbolic coxeter group, planar hyperbolic coxeter groups

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